无网格动力法中质量矩阵构造方法研究
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摘要
无网格动力法中质量矩阵的构造对计算结果的精度有着重要影响。本文就无网格动力法中质量矩阵的构造方法,给出了一致质量矩阵和集中质量矩阵的数学表达式,运用MATLAB软件编制了基于不同质量矩阵的无网格动力法计算程序,对无约束矩形板不同质量矩阵构造下的频率和振型进行了对比计算。结果表明:采用集中质量矩阵时,结果受节点划分的影响较大,只有节点划分足够密集时,结果才趋于精确值;而采用一致质量矩阵时,结果受节点划分的影响较小,说明了一致质量矩阵在无网格动力法质量矩阵构造中的优越性。
The structure of the mass matrix in the meshless dynamic method has important influence on the accuracy of the calculation results.This paper presents the method for construction of mass matrix in the meshless dynamic method.The MATLAB software is used to compile the meshless dynamic calculation program based on the different mass matrix.The frequency and mode of the structure of the different mass matrices of the unconstrained rectangular plate are calculated and compared.The results show that the lumped mass matrix and the affected node partition is large,and that only when the node is dense enough,the result tends to the exact value;the consistent mass matrix being adopted,the affected node partition is small,showing the superiority of the consistent mass matrix in grid power quality in matrix structure.
The structure of the mass matrix in the meshless dynamic method has important influence on the accuracy of the calculation results.This paper presents the method for construction of mass matrix in the meshless dynamic method.The MATLAB software is used to compile the meshless dynamic calculation program based on the different mass matrix.The frequency and mode of the structure of the different mass matrices of the unconstrained rectangular plate are calculated and compared.The results show that the lumped mass matrix and the affected node partition is large,and that only when the node is dense enough,the result tends to the exact value;the consistent mass matrix being adopted,the affected node partition is small,showing the superiority of the consistent mass matrix in grid power quality in matrix structure.
引文
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[2]LI Shaofan,LIU W.Meshfree and particle method and their applications[J].Applied Mechanics Review,2002,55(1):1-34.
[3]李卧东,王元汉,谭国焕.无网格法在弹塑性问题中的应用[J].固体力学学报,2001,22(4):361-367.LI Wodong,WANG Yuanhan,TAN Guohuan.Application of meshless method to elastoplastic problems[J].Chinese Journal of Solid Mechanics,2001,22(4):361-367.
[4]程玉民,陈美娟.弹性力学的一种边界无单元法[J].力学学报,2003,35(2):181-186.CHENG Yumin,CHEN Meijuan.A boundary-free method for linear elasticity[J].Chinese Journal of Theoretical and Applied Mechanics,2003,35(2):181-186.
[5]胡可.基于有限元方法一致质量矩阵的分析与计算[J].煤炭技术,2012,31(1):170-172.HU Ke.Aanaltsis and calculation of consistent mass matrix based on finite element method[J].Coal Technology,2012,31(1):170-172.
[6]苗雨,王元汉.弹性动力学的双互易杂交边界点法[J].力学学报,2009,41(1):122-128.MIAO Yu,WANG Yuanhan.Dual reciprocity hybrid boundary node method for elastodynamics[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(1):122-128.
[7]陈莘莘,李庆华,刘应华,等.动力弹塑性分析的无网格自然单元法[J].固体力学学报,2011,32(5):493-499.CHEN Shenshen,LI Qinghua,LIU Yinghua,et al.Applicatiom of meshless natural element method to dynamiac elastoplastic analysis[J].Chinese Journal of Solid Mechanics,2011,32(5):493-499.
[8]李树枕,李术才,朱维申.弹性动力学的无网格流形方法[J].岩土力学与工程学报,2006,25(1):141-145.LI Shuzhen,LI Shucai,ZHU Weishen.Study on meshless manifold method in elastodynamics[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(1):141-145.
[9]左占宣,李爽,翟长海.建立基于力的变截面梁单元质量矩阵的新方法[J].计算力学学报,2013,30(5):744-748.ZUO Zhanxuan,LI Shuang,ZHAI Changhai.A new method of formulating the consistent mass matrices for force-based beam elements[J].Chinese Journal of Computational Mechanics,2013,30(5):744-748.
[10]姚涛,段国林,张家谔,等.基于集中质量法的普通圆锯片及开槽圆锯片振动响应分析[J].应用力学学报,2015,32(3):496-501.YAO Tao,DUAN Guolin,ZHANG Jiae,et al.Application of concentrated mass method to vibration response analysis for slotted circular saw blade[J].Chinese Journal of Applied Mechanics,2015,32(3):496-501.
[11]刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005:17-20.